Weibull MTBF

Weibull distribution mean: MTBF = η · Γ(1 + 1/β). Useful when β ≠ 1 (wear-out or infant-mortality).

MaintenanceWeibull

Scale ηhShape β - β<1 infant mortality; β=1 constant rate; β>1 wear-out. Bearings β≈2–3; gears β≈3–4.

Γ(1 + 1/β): 0.8873 -

MTBF: 4,436h

Changing the inputs requires JavaScript. The calculator above shows its default inputs and result. The formula, symbols, and regulatory sources are shown in the Formula section below.

Formula, assumptions, and limits

\text{MTBF} = \eta \cdot \Gamma\!\left(1 + \tfrac{1}{\beta}\right)

Symbol	Meaning	Unit
$η$	Weibull scale	h
$β$	Weibull shape
$Γ$	Gamma function

Source: Abernethy - The New Weibull Handbook

In short

Weibull distribution mean: MTBF = \u03b7 \u00b7 \u0393(1 + 1/\u03b2).

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